Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [optimization]

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

In mathematics, computer science, economics, or management science, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.

An optimization problem can be represented in the following way: given a function $f:A\to\mathbb{R}$ from some set $A$ to the real numbers, we want to find an element $x_0\in A$ such that $f(x_0)\le f(x)$ for all $x \in A$ ("minimization") or such that $f(x_0)\ge f(x)$ for all $x \in A$ ("maximization").

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What operation is this in maths

I need to develop an algorithm for a problem then translate it into code, but I am sure someone would had done it before, my question is that what is the name of operation in below sudo code ? var a = [1]; // or it can be x1 var b = [1,2]; // or it…
Mathematics
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How to read 3 dimensional parameter from Excel to GAMS?

I don't know it is the place to ask this GAMS question but I couldn't find any other source. My question is about reading 3 dimensional parameter to GAMS from Excel file. I know it if there is a 2 dimensional parameter we should use; parameter t(i,…
Ali Tor
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Find the minimum value of $P=x^2+y^2+\frac{x^2y^2}{(4xy-x-y)^2}$

Given that $\frac{1}{3}
tangkhaihanh
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Min and max with two constraints (Lagrange Multipliers)

I should find the minimum and maximum values of $f(x,y,z)=x+y+z$ given the constraints $x^2+y^2+z^2=1$ and $x−y-z=1$. I found here a same exercise, but I don't know how the define the value of $x$, $y$, $z$.
Evelin Danás
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Why this two problems are equivalent?

I was reading about Support Vector Machines and I found that it's equivalent to solve the problem of maximize this number: $\frac{1}{\left \| w \right \|}$ with to minimize this number: $\frac{1}{2}\left \| w \right \|^{2}$ I would like to…
neo33
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Minimum of a bivariate quadratic function

According to (hope my calculation below is correct) https://en.wikipedia.org/wiki/Quadratic_function a bivariate quadratic function is a second-degree polynomial of the form $$ f(\xi,\eta)=\mathcal{A}\, \xi^2 + \mathcal{B}\, \eta^2 + \mathcal{C}\,…
LCH
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What would be the formula to optimize RPS vs. Latency?

I am trying to come up with a cost function that I could minimize/maximize. This would be a two variables function: number of requests per second and latency in ms. What we observed is that the more requests we serve, the higher the latency. We want…
Martin
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Dealing with non-negativity constraints without using Kuhn-Tucker conditions

Suppose I wish to maximize the function $f(x,y)$ subject to the equality constraint $g(x,y)=c$ as well as the non-negativity constraints $x\geq0$, $y\geq0$. If I first solve it ignoring the non-negativity constraints and find that $x<0$ and $y>0$…
hk39
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Maximize $|Ax|/N$ for binary $x$

Is there a systematic way of going about solving \begin{align} {\text{maximize}} &\hspace{3mm}& \frac{|\mathbf{Ax}|}{N} \\ \text{subject to} &\hspace{3mm}& \mathbf{x} = [0,1] \end{align} where $N$ is the number of non-zero elements in $\mathbf{x}$?…
user173690
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Where do we use the fact that we chose $b \geq 0$ in $P$ of the general primal-dual algorithm?

It's in in the general primal-dual algorithm and I don't know why we choose $b \geq 0$ in $P$. I guess it may be related to the RP problem but I am not sure because I don't not have a deep understanding of it. Thanks a lot. Starting with an LP…
Ben Lau
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Optimizing expected sale price by dynamic programming

I would like to sell my computer to the highest bidder. I have studied the market, and concluded that I am likely to receive three types of offers: an offer of \$200 dollars with probability $2/7$, an offer of \$300 dollars with probability $4/7$,…
foley
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What is the optimization formulation of this question?

I found the following puzzle on SO: Puzzle: A merchant has a 40 kg weight which he used in his shop. Once, it fell from his hands and was broken into 4 pieces. But surprisingly, now he can weigh any weight between 1 kg to 40 kg with the…
Legend
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Maxima and minima of parallelopiped

Show that a box (rectangular parallelopiped) of maximum volume V with prescribed surface area is a cube. Let $$V=xyz$$ $$S=2xy + 2yz + 2zx$$ $S$ is constant. Using Lagrange method, I am stuck at $V_x$$_x$=$0$=$V_y$$_y$=$V_z$$_z$ at the (only)…
T.Pal
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can I use interior-point method to solve binary decision problem?

I have an optimization problem formulated as follows. Let optimization function be defined as: maximize $\sum_j \sum_w f(_{,}\cdot \mbox{}) + g(_{,})$ subject to: $\sum_w _{,}\cdot _{,} \cdot _{,} \leq _ \left(\forall , \forall \right)$ is a binary…
Muhammad asif raza
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Maximizing of a two-variable function

It is very critical to find the maximum of the following function. Assume that m_{1}, m_{2} and m are constants: $f(x,y)=\frac{m_{1}x^4+m_{2}y^4+x^2+y^2-x^2y^2}{x^2+y^2-mx^2y^2}$ I tried to to compute gradient and then find the critical points but I…
user160492
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